Two-dimensional trajectory optimization of stratospheric airship

An asymptotical trajectory optimization method is proposed to solve the two dimensional trajectory optimization problem on circumstances that the singular perturbation is inapplicable, generally because the time scales of the motion model is not of different order of magnitude. Finding the cause of the coupling between velocity and sideslip angle is the exist of induce drag, the path can be optimized by neglecting the induce drag in the first step. Without the effect of thrust, it can be proved that the shortest path is the optimal one. And this shortest path is defined as the zero order solution. In the second step, basing on the path determined in zero order solution, and reconsidering the induce drag at the same time, the thrust can be optimized, and this optimal thrust is called the quasi first order solution. In the last step, the sideslip angle is re-optimized basing on the optimal thrust achieved in the quasi first order solution, and the result is called first order solution. As well, on this basis, a method to solve the trajectory optimization problem in a constant wind is proposed. In the end, the numerical example proves the superiority of the asymptotical method comparing with singular perturbation method, and shows the feasibility of this method under the condition of constant wind.